Question 636453: Find the center, foci, vertices, and asymptotes. Please show all your steps.
y^2/25-x^2=1
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the center, foci, vertices, and asymptotes. Please show all your steps.
y^2/25-x^2=1
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This is a hyperbola with vertical transverse axis.
Its standard form of equation  , (h,k)=(x,y) coordinates of center
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For given equation of a hyperbola:
center: (0,0)
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a^2=25
a=√25=5
vertices: (0, 0±a)=(0, 0±5)=(0,-5) and (0,5)
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b^2=1
b=1
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c^2=a^2+b^2=25+1=26
c=√26≈5.1
Foci: (0, 0±c)=(0, 0±5.1)=(0,-5.1) and (0,5.1)
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Asymptotes are lines that intersect at center (0,0). Equation: y=mx+b, m=slope, b=y-intercept
slopes of asymptotes of hyperbolas with vertical transverse axis=±a/b=±5/1=±5
Equation of asymptote with negative slope (-5)
y=-5x+b
y=-5x+0
y=-5x
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Equation of asymptote with positive slope (5)
y=5x+b
y=5x+0
y=5x
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